tl:dr: to ensure a positive result, have an observing plan and some background information before the first observing session to avoid disappointment!
If one looks for those beautiful planet images one will be disappointed. But if one is looking for many different interesting things because one knows ahead of time what to look for, it will be much more fun!
A low quality telescope will be disappointing compared to a good quality one; a used good quality telescope might end up a much better deal than a new low quality one of the same price, but buy from an owner who can show you how to set it up. Look for an astronomy club if possible, they don't need to be necessarily local, but having an experienced observer give you some coaching or help you find a new or used scope in your price range could really help.
@Woody's answer is very helpful, it's a good idea to manage expectations.
Worst case scenario is that you spend some money and time getting a great telescope, your child takes a few looks, sees a fuzzy, dancing blob of light, says "oh", runs back inside to some instantly-gratifying electronic device and that's the end of it, except you just put all that time and money into buying that great telescope...
I'd encourage you to manage expectations and (potentially) make the experience a lot more fun/rewarding by doing some reading or watching videos about amateur observing.
In addition to the planets, there are other potentially more beautiful things to look for!
As we are coming into winter soon and you are in the Northern hemisphere, why not learn a few constellations too. Orion is a big favorite because it is easy to recognize with those three stars that make up the belt, and the "sword" contains the great Orion nebula which will already look good in binoculars and really could benefit from the higher magnification of a telescope if you decide to go that way.
Betelgeuse, the bright orange star (yes, some stars have obvious color!) that makes up one corner of the big rectangle that is Orion has been in the news a lot lately, you could read about that so that it has some context.
Then there are the beautiful Pleiades that can be found by extending a line along the three stars of the belt. Learning/reading a little bit about them may also make finding them and looking at them more interesting.
The Big Dipper is another favorite, and the stellar system of Mizar and Alcor can be resolved with even a small pair of binoculars. What's exciting to learn here is that each of those is also a double start; there are four stars doing an elaborate dance together!
In fact, many and perhaps most stars are part of multiple star systems, and our singleton Sun is a little bit unusual that it has no companion!
For Jupiter, what's more fun than the blob itself is the four Galilean moons that dance around it. These are easy to see in binoculars and every night they will be in noticeably different positions!
You can find their positions online first if you like, or what may be more fun is to try to sketch their positions; draw a circle for Jupiter and use it to estimate how far the "little stars" are from it. They will all pretty much fall on one like through the Jupiter's equator, which helps distinguish them from stars.
To get an idea where things will be and to plan your evening I recommend either the website in-the-sky.org which has news, observing suggestions and a planetarium mode (it will get your general location and time zone from your internet connection, but as shown in the screenshot below you can also reset it to wherever you like.)
The other, even more fun way would be to download some free planetarium software. I notice that Stellarium seems to be mentioned frequently in this site and used to answer many questions here for example.
If the telescope or binoculars are meant to be a surprise, then trips to a library to read about Astronomy or viewing videos on Youtube together ahead of time may not be possible, but you can certainly plan ahead and have some of those at least ready.
For more options on apps and website etc. have a look at the answer to Where can I find the positions of the planets, stars, moons, artificial satellites, etc. and visualize them?
You can also search right here in Astronomy SE for information or ask questions, and if the first observing sessions generate questions you can also consider posting them here, e.g. "what did we see?" or "why couldn't we see...?"
I've chosen Riga as the location and
25-Dec-2021 22:00 EET as the date and time. I then typed "Pleiades" in the Find box to make them easier to see.
Christmas night 2021 in Latvia, 10 PM local time: